Proportion

Galileo• Was unable to measure the

acceleration of gravity accurately. a = g = 9.80 m/s²

Discovered• Change in velocity is

proportional to the time elapsed.

• Δv ~ t

Proportion• When I was growing up• Little girls played with dolls• 1959 !• Barbie• Proportion• Head to height– Baby 1:3– Adult woman 1:7

• A Proportion Equal Ratios

Head HeightAdult 9" 63"Barbie 2" 14"

Prob Set 1Q

It’s about the Relationship

• The greater the force, the greater the stretch

• Force ~ Stretch• F ~ x or F α x • F = k x∙• F1/x1 = k = F2/x2

• F1/x1 = F2/x2

• x2/x1 = F2/F1

• x2 is to x1 as F2 is to F1

Blue is to pale blue as red is to __________

The Stretch is Proportional to the Force

We can use Any Units

F1/x1 = F2/x2 20 pounds is to 4 inches as 10 pounds is to 2 inches20 lbs : 4" :: 10 lbs : 2"

F2/F1 = x2/x1

20 lbs is to 10 lbs as 4 inches is to 2 inches 20 lbs : 10 lbs = 4" : 2“ = 2 pure number

Prob Set 14B

Pressure and Volume areInversely Related

• When the volume goes down, the pressure goes up

• Pressure is inversely proportional to volume

• P ~ 1 / V• P = k / V• P1V1 = k = P2V2

• P1V1 = P2V2

• P1/P2 = V2 /V1

Direct: F1/x1 = F2/x2

Inverse: P1V1 = P2V2

or: P1/P2 = V2 /V1

Prob Set 14G

A Scale Drawing is in Proportion

4" x 10"

6" x 15"Both Ratios are 2 : 5